Question

A convex polyhedron has faces that consist of 30 squares, 20 hexagons, and 12 octagons. The polyhedron has 120 vertices. How many edges does it have? Euler’s formula: V + F = E + 2

Answer 1

180 is correct

Explanation:

Answer 2

Add the total faces: 30 + 20 + 12 = 62

Using the given equation: V + F = E +2

You have F = 62, V = 120

Now solve for E:

120 + 62 = E +2

Simplify:

182 = E +2

Subtract 2 from both sides:

E = 182 - 2

E = 180

It has 180 edges.